| A solid sphere of mass M and radius R is placed on a smooth horizontal surface. It is given a horizontal impulse J at a height h above the centre of mass and sphere starts rolling then, the value of h and speed of centre of mass are - |
 |
A) \[h=\frac{2}{3}R\] and \[v=\frac{J}{M}\]
B) \[h=\frac{2}{5}R\] and \[v=\frac{2}{5}\frac{J}{M}\]
C) \[h=\frac{7}{5}R\] and \[v=\frac{7}{5}\frac{J}{M}\]
D) \[h=\frac{7}{5}R\] and \[v=\frac{J}{M}\]
Correct Answer: A
Solution :
| Let the force producing impulse J is F then |
| \[{{\tau }_{about}}C=I\alpha \] |
| \[\tau \] and \[F=M\alpha \] (where a= R\[\alpha \]) |
| \[\therefore \,\,\,M\alpha h=\frac{2}{5}MRa\] \[\Rightarrow h=\frac{2}{5}R\] |
| Also impulse = change in momentum |
| Or \[J=Mv\] |
| \[\therefore \,\,\,\,\,\,\,v=\frac{J}{M}\] |
You need to login to perform this action.
You will be redirected in
3 sec
